78 QUANTUM THEORY
increased; because then the Z electrons of the atom give rise to scattered
waves more or less in the same phase; thus the amplitude of the resultant
is proportional to Z and the intensity is proportional to Z 2 .
We do not suppose that free electrons scatter continuously in the
manner here investigated. Actually some electrons scatter whole quanta
and others are idle. But by the correspondence principle (53-1) is the
limit to which the true formulae must tend when each electron is scattering 5
many quanta; and it is customary to entertain the optimistic view that togei
such formulae will apply without grave inaccuracy a long way short of or o 1
the limit. with
For very short wave-lengths (e.g. y rays) the scattering coefficient is resul
less than 0 - 2 . This is associated with the fact that the electron acquires A
a velocity comparable with the velocity of light when it scatters a quantum the g
of such radiation; its inertia increases, and other complications of the react
problem ensue. force
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55
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